Aggregation steady state

It is assumed that irreversible aggregation occurs on contact. The rate of coagulation is expressed as the aggregation flux J of particles towards a central particle. Using a steady-state approximation, the diffusive flux is derived to be... 

Hounslow, M.J., 1990b. Nucleation, growth and aggregation rates from steady-state experimental data. American Institution of Chemical Engineers Journal, 36, 1748-1753. 

From the mechanism and values of the rate constants, the formation of B occurs very rapidly within a few hundred picoseconds and AB is formed on the microsecond time scale. These species exhibit characteristic absorption bands in the 550 to 600 nm region of the spectrum. At very long times, i.e. several seconds of steady state irradiation, the red shift in the absorption band is complete and presumably due to AnB as suggested by Krongauz (1 —2) Thus far, it has not been possible to clearly time resolve the formation of aggregates from AB dimers, although subtleties in the transient absorption indicate this is occurring. For instance, the time resolved buildup in absorbance at the red end of 600 nm band seems to be slower than it is 10 or 20 nm further to the blue. This may indicate a process such as ... 

As shown in double-blind, placebo-controlled, randomized studies with healthy subjects, both infused [145] and oral [146] L-arg significantly inhibited (by =40%) ADP-induced platelet aggregation in vitro and potentiated platelet cGMP content. The effect, though, was weak the plasma concentration of L-arg required to produce an anti-platelet effect was some 2-fold above normal, steady-state levels, and the oral anti-aggregatory L-arg dose was 4-fold greater than the usual daily L-arg intake in humans. The infused L-arg dose that effectively inhibited platelet activity (30 g total) was hypotensive and increased heart rate, whereas the oral anti-platelet dose (7 g per day over 3 days) did not affect blood pressure, suggestive of oral L-arg platelet selectivity. 

In addition to the determination of distances at a supramolecular level, RET can be used to demonstrate the mutual approach of a donor and an acceptor at a supramolecular level as a result of aggregation, association, conformational changes, etc. The donor and acceptor molecules are generally covalently linked to molecular, macromolecular or supramolecular species that move toward each other or move away. From the variations in transfer efficiency, information on the spatial relation between donor and acceptors can thus be obtained. Because of its simplicity, the steady-state RET-based method has been used in many diverse situations as shown below5 . 

The IC, values of the vinca binary alkaloids for microtubule assembly were measured from their concentration-dependent effects on steady-state turbidity levels. Values are presented from two separate experiments. The products induced by a high concentration (10 M) of each compound with MTP or steady-state microtubules assembled from MTP were determined by transmission electron microscopy of steady-state solutions from at least two separate preparations of protein with similar results. SA, Spiral aggregates S, single spirals Am. amorphous aggregates MT, microtubules N.D., not determined. 

Turro and Yekta [142] discussed a simple method for measuring aggregation number by steady-state fluorescence. In this method, the decrease of the fluorescence intensity of a micelle-bound probe is monitored as a function of the quencher concentration and is fitted to the equation [143]... 

In most processes, steps 1, 3, 5 and 6 are in pseudo steady state and the mass transfer is governed by diifusion through the gas-liquid layers (steps 2 and 4). An additional step can appear if one deals with aggregates of cells (pellets), but we will not examine this case. 

Transition from non-metallic clusters consisting of only a few atoms to nanosized metallic particles consisting of thousands of atoms and the concomitant conversion from covalent bond to continuous band structures have been the subject of intense scrutiny in both the gas phase and the solid state during the last decade [503-505]. It is only recently that modern-day colloid chemists have launched investigations into the kinetics and mechanisms of duster formation and cluster aggregation in aqueous solutions. Steady-state and pulse-radiolytic techniques have been used primarily to examine the evolution of nanosized metallic particles in metal-ion solutions [506-508]. 

The rate of oil drop aggregation/coalcscencc was measured independently from removal by the air bubbles by simply shutting off the air supply. For each experiment the steady-state inlet and outlet drop populations for each drop size were measured first with the air flowing into the cell then with no air flow. Table 3 presents representative experimental results. For each run, the net observed removal rate (Ra) and the removal rate due to drop aggregation/ coalescence (Pcp) were determined, thus enabling the calculation of the removal rate by air bubble flotation alone. The removal rate constants (K) for each oil drop size were computed for each run. 

In the asymmetric case (Da = 0) similar immobile particles A become aggregated in the course of reaction and, as t — oo, the relevant reaction rate no longer has steady-state but increases in time leading to the accelerated particle recombination (see also [79]). 

Note that equations (7.1.57) and (7.1.58) are of rather limited use since they are derived for large diffusion coefficients D when defect aggregation is not well pronounced. Moreover, equation (7.1.57) assumes existence of the steady-state for d = 2 whereas other methods discussed in [15] argue for the macroscopic defect segregation occuring here even for mobile defects. In this respect of great interest is the generalization of the more correct accumulation equations (7.1.50) to (7.1.52) presented below for the case of mobile defects. 

---